Probably the trapezoid is one of the most popular quadrilaterals when it comes to bridge construction. Numerous railroad trestles and wooden bridges of the nineteenth and early twentieth centuries were trapezoidal in shape.

In Figure 1, trapezoid *QRSV* is labeled so that *b*_{1} and *b*_{2} are the bases (*h* is the height to these bases) and *a* and *c* are the legs. The perimeter is simply the sum of these lengths.

**Figure 1 **A trapezoid and the associated parallelogram.

Referring to Figure , an identical, but upside‐down trapezoid is drawn adjacent to trapezoid *QRSV*, trapezoid *TUVS.* It can now be shown that the figure *QRTU* is a parallelogram, and its area can now be found.

Because trapezoid *QRSV* is exactly half of this parallelogram, the following formula gives the area of a trapezoid.

**Example 1:** Find the perimeter and area of Figure 2.

**Figure 2 **Finding the perimeter and area of a trapezoid.

The figure is a trapezoid.